stubbornp wrote:If an item that originally sold for z dollars was marked up by x percent and then discounted by y percent, which of the following expressions represents the final price of the item?
1.10,000z + 100z(x – y) – xyz/10,000
2.10,000z + 100z(y – x) – xyz/10,000
3.100z(x – y) – xyz/10,000
4.100z(y – x) – xyz/10,000
5.10,000/100yz + xy
Please explain...
We can do this either algebraically or by picking numbers. However, since the correct choice appears to be missing, picking numbers won't really work! We could also do this via common sense, an oft overlooked strategy on the GMAT.
Algebra:
If we mark up by x%, then we multiply by (100+x)/100.
If we mark down by y%, then we multiply by (100-y)/100.
So, our final price is:
(z)(100+x)(100-y)/(100)(100)
(100z + zx)(100-y)/10000
(10000z - 100zy + 100zx - zxy)/10000
10000z/10000 + 100(zx - zy)/10000 - zxy/10000
z + z(x-y)/100 - zxy/10000
which doesn't match any of your choices, which leads me to believe that you posted the answers incorrectly (because me making a mistake is unpossible! 8) ).
Common Sense
Anything with 10000z in it is WAY too big a number.
100z(x-y) or 100z(y-x) is either going to be super big positive or super big negative, also making no sense.
10000/100yx is equal to 100/yx. It's a safe bet that on test day, you won't see a non-reduced fraction as the correct answer.
So, using common sense we can elminate a, b, c, d AND e. Accordingly, choose:
(f) the correct answer is missing.
